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I wouldn't consider this a duplicate of the above mentioned question, since the linked to question is about Photoshop and this one makes no mention of such software. It is not safe to assume that all users have access to such expensive software.
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dpollittNov 20 '12 at 19:44

People use "in Photoshop" as a proxy for "with some sort of post-processing software" all the time. It happens that Photoshop doesn't do anything particularly magical in this area, so I think that one is fine as a generic question.
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mattdmNov 20 '12 at 19:57

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Have a look at onOne's Perfect Resize (formerly Genuine Fractals). Great piece of software with some handy features when doing prints. I agree that it's a dupe too...
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John Cavan♦Nov 21 '12 at 1:10

4 Answers
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It depends. If you have sufficient pixels for the size you need, than all you need is to change the DPI. So lets say you have a 12 megapixel image (4000 x 3000 pixels) at 300 DPI, then changing the DPI to 100 will make it 3 times bigger. This will take the 10" tall image and make it 30".

Should you judge that you do not have enough pixels, you need to interpolate the image. Most image processing software will do this and some have different algorithms, for example you will find something like Bicubic Smoother (Best for Enlargements) in Photoshop. Just enter your parameters in the Image Size dialog and let it do the work.

The number of pixels you need will depend on size and resolution. The resolution depends on viewing distance for your print. 300 DPI is common for small images which are seen closely and down to 150 DPI for poster-size is quite acceptable. In general, the larger the image, the further you look at it and the less resolution is needed.

Just a small note here for users of Ps CS6 (and, I'd assume, above when there is an "above"): the resize options now include a "Bicubic Auto", which does the smoother/sharper thing automatically depending on the new resolution, and does iterative up-rezzing so you don't have to do it manually anymore.
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user2719Nov 20 '12 at 19:58

Good to know. The CS6 box is still unopened here :)
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ItaiNov 20 '12 at 20:31

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@Itai - Open the box, it's a nice upgrade to have. Still, I think I'd go with onOne's Perfect Resize over the Photoshop options if it's more than a 50% increase in image size.
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John Cavan♦Nov 21 '12 at 3:33

There are many different free and paid software to do this and most of them have different algorithms to do so with various qualities.

As the process have to "guess" what happens between each the true pixels (that exist in the original) the chosen "interpolation filter" will make its own "assumptions" how to deduce from the neighborhood what happens. Each filter makes its own "artifacts" in the result.

As an example, in your case you want 300% size. That means that there are two unknown pixels between each true pixel:

I've implemented "Box" Nearest Neighbor (useful in some research cases because it never makes a pixel value that doesn't exist already), Hermite, Gaussian and Lanczos in Image View Plus More. I pick different filters to give me the result I think looks best in the given image.

It also has the feature to automatically do it incrementally in , say, 5-20% steps, as others recommend, instead of having to do this yourself, the program does it for you.

Will this method give "the best possible quality"?
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mattdmNov 20 '12 at 19:38

@mattdm - This is the quickest dirtiest way to make it happen. From reading the question I got the notion that the user might not know a whole lot about photography or image manipulation. Yes they asked for "best quality", but they also said "What method is common to become" which makes no sense at all. Sometimes we take answers waaay to far on this site when people want a simple "how do I do it the easiest/fastest way". The linked to question that you used as a possible dupe uses Photoshop, which many people don't have access to. Itai's answer is good, but goes in depth and can confuse some.
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dpollittNov 20 '12 at 19:43

Well, I have to admit, I think this is going to be fine on a billboard a hundred feet away, but not so much on a print that you'll hang on a wall. There are tools to do this at much higher quality, but they aren't free. Nevertheless, for quality, there are common options and OP didn't say it had to be cheap.
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John Cavan♦Nov 21 '12 at 3:31

Ugh whatever. You are right, lets just assume that everyone wants to spend $99 for Perfect Resize, or $699 for Photoshop, or $89 for PS Elements. Look at the wording of this question. They tagged it with "scale". The title is "How to scale up a photo?". My bet is that it someone completely unfamiliar and potentially not caring what DPI is. So explaining a verbose example of why DPI matters and what it is, etc might not help them whatsoever. They probably want to blow up a thumbnail that they have for Facebook! Not everyone is a programmer or has that mentality; or cares to be a pro photog.
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dpollittNov 21 '12 at 3:58

If you just want to blow up you dont even need xnview or any other software. MSPaint does this out of box what you have shown here.
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GoodSp33dNov 21 '12 at 9:29

This is based from some pro photogs and printer studio's that have been doing large scale billboards. What they recommend is to enlarge the image in Photoshop by 5-15% at a time. This is to avoid pixilating the image too much when Photoshop applies the enlargement to the image. The cause of this is how Photoshop enlarges the pics. They say PS makes the image bigger by creating spaces between pixels and filling those pixels up with what Photoshop assumes as the correct color for that space, based on the surrounding colors. Increasing it 5-15% at a time means that PS will only need to create and fill up a small space, making the rendition of the new colors in the space more accurate.